There are multiple, inequivalent, definitions for conjugacy in semigroups. In Cummings and Jackson (Semigroup Forum 88, 52–66, 2014), we conjectured that, for at least one of these definitions of conjugacy, the conjugacy problem for finitely presented semigroups satisfying C(2) and T(4) is solvable. Here we essentially verify that conjecture. In that 2014 Semigroup Forum publication, we developed geometric methods to solve a conjugacy problem for finitely presented semigroups satisfying C(3). We use those methods again here.
Conjugacy problem Semigroup diagrams Small overlap semigroups
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The first author would like to thank Maritza Martinez, Director of the Educational Opportunities Program, for supporting his request for a spring 2015 educational leave, in part, to begin work on this article. He would also like to thank his students and the staffs of the EOP and the Office of Access and Academic Enrichment for all of their encouragement and support.